The Secret of the West (Le Secret de l'Occident) quoted by Philipp Hoffman in California in an on-line paper about the causes of the Western miracle (shortcut 1, shortcut 2). PDF-version of article. Unfortunately, P. Hoffman misquotes this book, being mistaken about its philosophy. Besides, he does not realize that his own idea, and much more, is already encompassed in The Secret of the West.
(Philipp T. Hoffman: "Why Is It That Europeans Ended Up Conquering the Rest of the Globe? Prices, the Military Revolution, and Western Europe’s Comparative Advantage in Violence", 23 October 2006)

Safety copy: August 2007. Source
The Secret of the West

Why Is It That Europeans Ended Up Conquering the Rest of the Globe? Prices, the Military Revolution, and Western Europe’s Comparative Advantage in Violence
Why Is It That Europeans Ended Up Conquering the Rest of the Globe?
Prices, the Military Revolution, and Western Europe’s Comparative Advantage in Violence

Philip T. Hoffman
California Institute of Technology
HSS 228-77 Pasadena, CA 91125 USA
October 23, 2006

Why did Europeans conquer the rest of the world? The likely cause was a tournament among
western European rulers that fostered military innovation. Price data from England, France, and
Germany support such an argument, as do physical measures of military productivity; they show
that the military sector in western Europe was experiencing rapid and sustained technical change
well before the Industrial Revolution. The price data shed new light on this military revolution
and its economic consequences. Comparisons with the rest the world explain why it was
peculiar to Europe and why it gave western Europe a comparative advantage in violence.
In recent years, historians, economists, and other social scientists have
energetically debated when Western Europe first forged ahead of other parts of the
world–in particular, advanced parts of Asia–in the race toward economic development.
Was it only after 1800, with the Industrial Revolution well underway, that Western
European per-capita incomes, labor productivity, or technology diverged (Wong 1997;
Pomeranz 2000; Goldstone forthcoming)? Or was it earlier, before the Industrial
Revolution (van Zanden 2003; Allen 2005; Broadberry and Gupta 2005)? And what was
the cause of the divergence? Was it beneficial institutions, which encouraged investment
and the accumulation of human and physical capital (North and Thomas 1973; North and
Weingast 1989; Acemoglu, Johnson et al. 2002)? The Scientific Revolution and the
Enlightenment, which spread useful knowledge and political reform (Jacob 1997; Mokyr
2002; Cosandey 1997)? Or was it simply an accident that the Industrial Revolution
started in Western Europe (Clark 2003)?
In this debate, one area in which Western Europe possessed an undeniable
comparative advantage well before 1800 seems to have been overlooked–namely,
violence. The states of Western Europe were simply better at making and using artillery,
firearms, fortifications, and armed ships than other advanced parts of the world and they
had this advantage long before 1800. By 1800, Europeans had conquered some 35
percent of the globe, and they controlled lucrative trade routes as far away as Asia
(Parker 1996, 5). Some of the land they subjugated had come into their hands because of
new diseases that they introduced into vulnerable populations, and in these instances–in
the Americas in particular–their advantage was not military, but biological (Diamond
1997). But other inhabitants of densely populated parts of Eurasia would have had the
same biological edge. Why was it therefore the Western Europeans who took over the
Americas, and not the Chinese or the Japanese?
The history of conquest is not the only evidence for Western Europe’s military
advantage before 1800. States elsewhere–China, Japan, and the Ottoman Empire–
certainly possessed firearms or ships equipped with artillery, but by the late seventeenth
century, if not beforehand, nearly all of them had fallen behind in using this technology.
The case of the Ottoman Empire is illustrative. There the military gap may reach back as
far as 1572, when Venetian cannon founders judged that guns captured during the naval
battle at Lepanto were simply not worth reusing. The Ottoman cannons had to be melted
down–and new metal had to be added to the mixture–because “the material is of such
poor quality.” (Mallett and Hale 1984, 400).
At a time when the high cost of
manufactured goods meant everything was salvaged—even clothing from fallen
comrades—that amounts to strong evidence from revealed preference about how much
better Western European weapons had become. The history of trade and of the migration
of military experts points in the same direction. Although the Ottomans could threaten
Vienna as late as 1683, they were importing weapons from western Europe and often
relied on the expertise of European military specialists.
The Ottoman Empire was hardly exceptional. From the Middle East to East Asia,
experts from Western Europe were hired in Asia to provide needed help with gun
making, tactics, and military organization. They ranged from renegade European gun
founders in the sixteenth century to Napoleonic officers the early 1800s. In seventeenth-
century China, even Jesuit missionaries were pressed into service to help the Chinese
Emperor make better cannons. The evidence for Western Europe’s military prowess is so
strong that it has even convinced some of the historians who argue against any
divergence between Western Europe and advanced areas of China before 1800.
Although they would argue that Western Europe was not wealthier or more developed
than rich areas of China, they would acknowledge that its military technology was more
advanced (Wong 1997, 89-90; Pomeranz 2000, 199-200).
The evidence is thus fairly clear, but it is nonetheless surprising that western
Europe had come to dominate this technology of gunpowder weapons so early. Firearms
and gunpowder, after all, had originated in China and spread throughout Eurasia. States
outside Western Europe possessed the revolutionary weapons and did become, at least for
a while, proficient at manufacturing or exploiting the new military technology. The
Ottomans, for instance, made high quality artillery as late as the 1500s. The Japanese
independently discovered, at about the same time as Western Europeans, the key tactical
innovation (volley fire) that allowed infantry soldiers with slow loading muskets to
maintain a nearly continuous round of fire.
Yet by the late seventeenth century, if not
before, Chinese, Japanese, and Ottoman military technology and tactics all lagged far
behind what one found in western Europe.
Why did these other powerful states fall behind? Apart from Carlo Cipolla’s
(1966) pioneering effort some 40 years ago, economist historians (and social scientists in
general) have not paid much attention to this question. Western Europe’s advances in
military tactics and technology have certainly attracted a number of talented military
historians and historians of technology, but their work ignores the economics, even
though they acknowledge that the cost of weapons fell.
What happens if we examine the
political economy of the military revolution and look in particular at prices of military
goods? What do they tell us about western Europe’s military growing military strength?
The price data, it turns out, offer some novel insights into the debates military and
technological historians have had over the nature of the military revolution. They also
carry the startling implication that Europe’s military sector could sustain technical change
for centuries–a feat virtually unknown elsewhere in pre-industrial economies. But their
greatest signifance lies with what they suggest is the underlying cause of Western
Europe’s comparative advantage in violence: a tournament among western European
rulers that fostered military innovation. Politics made that tournament peculiar to
western Europe and led the continent to dominate the technology of artillery, firearms,
fortifications, and gunships.

The Evidence from Prices

Suppose that we confine ourselves to examining the cost of producing the new
weapons that played a key role in military revolution–artillery, handguns, and
gunpowder. The question would be whether the cost curves for producing these military
goods are declining, once we take into account changes in other prices. If the cost curves
are shifting down, then the production functions for the weapons are moving out, and the
firms producing them are undergoing technical change.
This sort of exercise certainly has its limits and is probably biased against finding
any technical change. To begin with, it likely to underestimate the magnitude of the
military revolution. Ideally, we should be measuring the cost of attaining a given level of
military effectiveness, but we are instead simply gauging the cost of producing certain
military products, and only doing that once the products are available for sale in
sufficient numbers to leave a historical record. Restricting our attention to the products
leaves out tactical innovations, better training, and improvements in provisioning armies
and navies and in raising money to pay for military operations. And by omitting
advances in ship construction, seaborn strategy, and maritime forces’ ability to fight
around the globe and in bad weather, it glosses over most of naval warfare, where
western Europe’s comparative advantage was probably greatest. Similarly, waiting until
prices appear in the historical records is likely to omit the initial drop in the cost of
producing the weapons right after they were first introduced but before sales and cost
estimates left much of trace in the archives.
In an ideal world, we could put together a long, homogenous series of prices for
artillery, handguns, and gunpowder in countries across the world. Unfortunately, we are
not at that stage yet, in large part because prices for military goods–guns in particular–are
hard to come by.
For the moment at least, we have to make do with somewhat
fragmentary price data from several western European countries only–in particular,
England, France, and (for a smaller number of observations) Germany.
What then do the price data for artillery, handguns, and gunpowder from these
countries tell us? Let us begin by assuming that each of these goods is each produced by
cost minimizing firms that are small relative to the size of the market they sell in and that
entry into these product markets is open. Let us also assume that markets for the factors
of production are competitive and that the firms have U-shaped short run average cost
These are not unreasonable assumptions for England, France, and Germany.
Factor markets were competitive, and weapons production in these countries was, for the
most part, in the hands of a large number of small scale contractors and independent
craftsmen. Furthermore, entry into the weapons business did seem to be open, at least in
the long run. Craftsmen and contractors moved their production from city to city and
even migrated from country to country. While there were some signs of fleeting
collusion or high prices in England and France when their rulers wanted to nurture the
native arms industry, they seem to have been temporary, because major weapons buyers
(this was true in particular of governments) would go elsewhere if they thought prices
were high.
Under these assumptions, it will be difficult for weapons producers to collude,
and free entry will drive them to produce at minimum average cost. The long run
industry supply curve will then be flat, and the cost of producing a quantity y of our
military good at time t will be turn out to be y c(w, t), where c(w, t) is the minimum
average cost of producing the good and w is the vector of factor prices. The function c(w,
, which is also a firm’s marginal cost, will be independent of y but will depend on time
to allow for the possibility of technical change. If there is technical change, then c(w, t)
will be a decreasing function of t for any given w, and the partial derivative of its
logarithm will give the rate of technical change. (For technical details here and in what
follows, see the appendix.)
Because collusion will be difficult, the price p of the good produced will be the
marginal cost, or c(w, t). Provided that all of our assumptions held, we could therefore
test for technical change by regressing the price of each of our military goods on w and t.
All we would have to do is to choose a suitable functional form for c(w, t). Ideally, we
might want to use some flexible functional form, but lack of enough price observations
would probably limit us to deriving it from a Cobb-Douglas cost function, which would
at least be a first order approximation to c(w, t). The Cobb-Douglas technology will have
to constant returns to scale since the marginal cost is independent of output. If we adopt
the Cobb-Douglas functional form, and if the technology changes at a constant rate and is
cost neutral, then
ln (p) = ln (c(w, t)) = a - bt + s
ln (w
+ . . . + s
ln (w
+ u (1)
where a is a constant, b > 0 is the rate of technical change, u is an error term, s
and w
the factor share and price of the i-th factor of production, and the factor shares have to
add up to one. Equation 1 is equivalent to assuming that the good’s production function
is Cobb-Douglas with a multiplicative constant that grows at rate b. Because the factor
shares add up to one, we can single out one of the factor prices (say w
) and actually
estimate the following equation:
ln (p/w
) = a - bt + s
ln (w
) + . . . + s
ln (w
) + u (2)

where the only restrictions on the s
now are that they and their sum lie between zero and
Unfortunately, we do not yet have enough data to do that, although it may become
possible in the future as more prices become available.
But if we let w
be the price of
skilled labor (an essential input into weapons production), then we can at least calculate
and compare how it changes with the variation in the relative prices w
. If p/w
, the relative price of military goods relative to skilled labor, falls more
rapidly than the relative prices of the other factors of production, then we have evidence
for technical change in the military sector, and we can estimate how large the rate of
technical change must have been.
If Figures 1 through 5 can be trusted, the price of military goods seems to have
fallen relative to the cost of skilled labor and relative to the cost of major factors of
production used in producing weapons in both England and France. Prices dropped for
artillery, muskets, and pistols, and they did so as early as late Middle Ages. Of course,
one might want to add a rental price of capital to the figures, but if we make reasonable
guess at depreciation and suppose that the sales price of capital goods was proportional to
skilled wages, then the rental price of capital declines only slightly in the figures, and if
the capital is building space, its rental price may have actually risen sharply, at least in
some locations (Figures 6 and 7). What the figures suggest, therefore, is that the military
sector of the economy witnessed sustained technical change over a long period of time
before the Industrial Revolution.
We can get a sense of how large the technical change must have been if we take
our earliest and latest price observations for each military good and use equation (2) to
estimate an upper bound for how much of the change in the price can be accounted for by
shifts in the costs of the factors of production. We know how much ln(p/w
) changed
between the first and last observation, and we know how much the terms ln(w
changed too, at least for the factors of production listed in Table 1. Our coefficient b will
therefore equal
ln (p/w
) + s
ln (w
) + . . . + s
ln (w
) +
where Δ denotes the difference in each term between the initial and final period. This
expression will be greater than or equal to
ln (p/w
) + (1 – s
ln (w
) +
where s
is the factor share of labor and Δ
ln (w
is the smallest of the terms Δ
, . . . , Δ
ln (w
. If we take expectations (to make the Δu disappear) and
assume that the changes in the prices of the factors of production are all at least as large
as smallest one we can derive from Table 1, then we can calculate a lower bound for the
expected value of b simply by guessing at s
If we perform this calculation with a labor share of 0.5 (other reasonable labor
shares yield similar results), the resulting rates of technical change are nearly all larger by
preindustrial standards (Table 1). Apart from the 0.1 percent rate of change for French
muskets, the rates of growth in productivity are all over 0.5 percent per year, and the
figure is 0.9 percent for the manufacture of artillery in late medieval England. These
numbers compare favorably with rates of long run total factor productivity growth
elsewhere in the preindustrial world, which usually did not exceed 0.1 percent per year, at
least in sectors of the economy as large as the military one was in early modern Europe.
There were some exceptions to this rule–English agriculture, for instance, which seems to
have sustained long term total factor productivity growth rates of 0.2 to 0.3 percent per
year–but in most sectors of the preindustrial economy, faster growth could simply not be
Even during the Industrial Revolution, total factor productivity growth in
Britain seems to have hovered between 0.1 percent per year and 0.35 percent per year.
How could the defense industry do so well over such long periods of time, and in two
economies–France and England–that for most of the years in the table were largely pre-
One could of course argue that all the evidence here is a chance result, because it
all depends on initial and final price observations, which could vary randomly and be
buffeted about by the costs of factors of production that remain unobserved.
If we
enough data, we could settle the issue by estimating equation (2) and testing hypotheses
about the sign and magnitude of the coefficient b. But we cannot do that, even with
statistical methods that make up for missing data.
One thing we can do, however, is to compare the price of our military good with
that of a similar civilian commodity that involved a similar production process.
If the
civilian commodity was made with similar factors of production and similar factor
shares, and if the same economic assumption held for it too (small firms, open entry, U-
shaped short run average cost curves, competitive factor markets, and a Cobb-Douglas
production function), then equation 2 would apply to its price q too, and the logarithm of
p/q would be:

ln (p/q) = c - dt + e
ln (w
) + . . . + e
ln (w
) + v (3)

Here c is a constant, d is the rate of technical change for the military good minus that for
the non military good, v is an error term, and the e
’s are differences in the factor shares
for the two goods. If the factor shares for the two goods are nearly equal, then the e
will be close to zero, and
ln (p/q) ≈ c - dt (4)

We could then regress ln (p/q) on time and come up with an estimate for d, the rate of
technical change for our non military good less that for our non military good. The
estimate will be biased because the variables ln (w
) will be omitted from the
regression, but because the e
’s are small, the bias will be small too and may be either
positive or negative.
If production of the non-military good does not experience any
technical change, then d will be close to the rate of technical change b for the military
good. If there is technical change in production of the military good, the d we get from
equation (4) is likely to underestimate the rate at which the cost is declining. The key, of
course, will be finding non-military goods with factor shares similar to those of the
military goods–ideally, non-military goods whose production functions did not change.
This we can actually do, although we have to keep in mind that the coefficients
and estimated standard coefficient errors may be biased in an unknown way. In addition,
if we have prices of the factors of production for which the share differences e
are likely
to be relatively large, we can add them to the regression since they are likely to bias our
estimate of d the most.
The advantage of doing so is that we can find prices for factors
such as iron or capital, which may be used more intensively in either the military or
civilian good. We can include prices for these factors in a regression of ln (p/q) on a
constant and time and assume that the small e
’s for the other omitted variables will keep
their contribution to the bias small. That amounts to running regression (3) with some of
the ln (w
) omitted, but it is possible to run such a regression when it would be
impossible to get enough data to run a regression with all the variables ln (w
Table 2 shows what happens when we run either a regression based on equations
3 (with some missing variables) or equation 4. Again, the regressions involve the prices
of French and English handguns and artillery from the late Middle Ages to the eighteenth
century, and now gunpowder is included too. The prices of the English military goods
are expressed relative to the cost of spades, a non-military good that presumably had
factor shares roughly similar to those involved in the production of handguns, for like
spades, handguns were made of wood and metal. Admittedly, the factor shares were
probably different for artillery and gunpowder, and it no doubt took more metal to make a
firearm than a spade. But even cannons had wooden carriages, and wooden and metal
tools were used to manufacture gunpowder. Despite these disadvantages, though, using
the price of spades has certain virtues. Technical change in their production was
probably small before the eighteenth century, and there are repeated price observations
for spades with relatively little price variation at any given time. And where we have
enough data, we can compensate for the different factor shares for iron in military goods
by adding the relative price of iron to the regressions.
For French military goods, prices are compared to the cost of lathing nails.
Although the price of something like spades might have been a better non-military
yardstick for handguns, it proved impossible to find prices for spades or any other good
made out of both wood and metal. Lathing nails, however, are not a bad choice for
artillery, or for handguns either. Like the fabrication of handguns, the making of nails
required metal and skilled labor and it also consumed wood for heating the furnaces.
Lathing nails also had to serve as the non-military good for gunpowder, but at least here I
could compensate for what were probably different capital intensities by adding the rental
price of capital. Because the technology of nail making may have changed beginning as
early as the seventeenth century, all of the comparisons between the price of nails and the
price of artillery, handguns, and gunpowder may well underestimate technical change for
the military goods.
Like the prices of arms and gunpowder, the prices of the various non-military
used as yardsticks were fragmentary and not available for the same years for which prices
of arms and gunpowder could be found.
To solve this problem, I took 50-year averages
of the lathing nails prices that served as the non-military yardstick, and 25-year averages
of skilled wages and iron prices. In England, I had to use 25-year averages for the price
of iron and spades.
In the regressions of ln (p/q), the coefficient of time (the –d in equations 3 and 4)
is negative for all the military goods except for French gunpowder, when its price relative
to the cost of nails is regressed on time alone (Table 2). With that exception, time always
turns out to have a negative coefficient, whether the regressions are run with time alone
or whether relative prices of some other factors of production are added. Graphs of ln
reveal a clear downward trend in the relative price of the military goods in nearly
every instance (Figures 8 through 14). The only exceptions are for muskets and
gunpowder in France, and the relative price of gunpowder price does at least drop first
and then rise before falling again.
The regressions, in short, nearly all point point to technical change, at rates
ranging as high as 2.4 percent per year and over periods stretching from the fourteenth to
the eighteenth century. The median rate of technical change in the regressions with the
year alone is 0.5 percent per year; if we look instead at regressions with prices of other
factors of production added, the median is 0.8 percent per year. Again, these numbers are
high relative to rates of total productivity growth elsewhere in the preindustrial world, or
even during the Industrial Revolution. How could the defense industry do so well over
such long periods of time, and in two economies–France and England–that for most of
the years in the table were largely pre-industrial?
Perhaps one should simply not believe the data. After all, the figures are
fragmentary, the number of observations is small, and there are a huge number of
assumptions involved. One could certainly worry that quality differences and biases
from omitted prices for factors of production would make all of the tables and regression
results purely random.
Suppose, however, that the negative time coefficients in the
regressions were purely random. How often would we expect to get that many negative
coefficients if we were simply drawing from a Bernoulli distribution with a probability of
getting a negative regression coefficient exactly half of the time? If we limit ourselves to
the 7 regressions on time alone, 6 of the 7 coefficients are negative, and if each
coefficient represents an independent draw, then the odds of getting six negatives by
chance are only 0.06. If we substitute the regressions with the relative prices of other
factors of production, all 7 time coefficients are negative, and the probability of getting
that many negatives by chance in independent draws from a Bernoulli distribution is only
We could raise the bar higher by asking whether the regression coefficients in
Table 2 would be likely to arise if we were drawing them randomly from a population
with median of negative 0.1 percent per year, or, in other words, from a population
presumably typical of the sort of slow technical change one would find in a pre-industrial
society. In the regressions on time alone, 6 of the 7 coefficients point to technical change
at a rate of 0.1 percent per year or more. The odds of that happening by chance in
independent draws from a Bernoulli distribution are 0.06. And if we substitute the
regressions with prices of other factors of production, all 7 regressions yield rates of
technical change of 0.2 percent or more per year. The probability of that happening by
chance are only 0.06, even if the coefficients are drawn from a population with a median
as high as 0.3 percent year.
Perhaps the regressions and tables are therefore telling us something. Perhaps the
figures they contain are not as unreliable as it might seem at first glance. After all,
careful reading of the sources (and in particular, sensitivity to changes of vocabulary) can
help guard against unsuspected changes in quality, and in any case the data are likely to
underestimate technical change because they involve no correction for progressive
improvements in quality.
There are a number of other reasons why the rates of
technical change are likely to biased downward as well. To begin with, the focus on
prices overlooks all the advances in military tactics, organization, and financing that
made the European military more effective and yet had nothing to do with the production
of military goods. Fortifications are a clear example: although construction techniques
may not have improved, the design of fortifications certainly had (to make them
impervious to artillery barrages), and so too had the fiscal apparatus the paid the bills.
Similarly, the prices we have chosen also gloss over naval warfare, where western
Europe’s progress and comparative advantage were probably greatest. And Tables 1 and
2 do not take into account all sorts of continued technical change in weapons production
during the eighteenth century: boring and turning of cannons, or the standardized
production of flintlock muskets with at least some interchangeable parts.
One last reason why our rates of technical change may be biased downward
deserves to be stressed too. It is the simple fact that price data for a new weapon (as we
noted above) will typically not appear in historical records until well after it is first
invented, and that means after the period when costs of production are likely to be falling
most rapidly thanks to learning by doing (Lucas 1993). Fortunately, we have one
instance where we can verify that this took place, for some of the first handguns that were
ever made–in this case, ones that the German city of Frankfurt had produced during the
years 1399-1431. Thanks to the meticulous research of Bernhard Rathgen, an artillery
officer and military historian who died in 1927, we actually have prices for the handguns,
along with the wages paid to the metal workers who cast them and the cost of the copper
which served as the raw material. These early guns resembled small cannons (Figure 15)
with barrels less than 500 millimeters long. Although they were not very effective,
German cities like Frankfurt bought them in large numbers.
For these early handguns in Frankfurt, we actually have enough data to estimate
equation (2) with prices for all the factors of production included among the explanatory
When we run the regression (Table 3), we end up with reasonable
coefficients (the factor share for copper is 0.307) and a rate of total factor productivity
growth of 3.0 percent a year, which is more rapid than what was achieved by the most
dynamic sector of the British economy–the cotton textile industry–during the Industrial
And we know why productivity was climbing so fast: the metal workers
were learning how to make the handguns with less copper, which cut the price of the
guns drastically (Figure 16). To us, such an improvement may seem obvious, but given
the frequency with which early cannons exploded and maimed gunners, it was a step that
the gunsmiths must have taken with a great deal of trepidation.
Finally, if we turn from prices to physical evidence of greater productivity, the
story is much the same: firing rates for guns increased, misfires diminished, and
inventions such as the bayonet made it possible for armies to do away with pikemen and
to arm more and more of their soldiers, all of which boosted armies’ labor productivity.
In the French army, the rate of successful fire per solder jumped perhaps 13-fold between
the early seventeenth century and the middle of the eighteenth century (Table 4), which
translates into labor productivity growth of 1.7 percent a year. Other physical measures
of productivity, such as the range of early cannons, also soared.
Firing rates and cannon
ranges bring us much closer to what we would ideally be measuring—military
effectiveness—and they in fact suggest that if effectiveness is the yardstick, then the
military’s labor and capital productivity were both increasing.

Implications for Military History and Economic History

To assert that military production experienced surprising technical change in late
medieval and early modern Europe would of course fit what military historians claim
when they write about the military revolution (Black 1991; Parker 1996). More evidence
is of course essential; I am currently gathering it in printed and archival sources. But
perhaps it is not too early to speculate a bit about what the price trends imply, both for the
military revolution and western Europe’s comparative advantage in violence, and for
more general issues in economic history.
For economic history, the big surprise is the evidence of sustained technical
change over perhaps four centuries before the Industrial Revolution and in a major sector
of the economy to boot. If further data bear out this conclusion and demonstrate that the
rates of technical change were substantially higher than the 0.1 percent or less that
characterized most preindustrial economies, then we will have something to explain.
What could possibly account for such unusual sustained growth before the nineteenth
One possibility would be the competition among European states, which fought
practically incessantly between the late Middle Ages and the end of the Napoleonic Wars.
Until the French Revolution, the states’ rulers (typically kings or princes) had every
incentive to fight: they bore little of the cost of a military buildup, and they were rarely
deposed or killed in case of defeat, at least in the major states (Table 5). The political
incentives and military competition gave rents to victors (control of lucrative trade routes,
for instance), and those rents would conceivably encourage military innovation, both in
the realm of military technology and in tactics and military organization.
So too would the glory and honor that most European rulers (and European
aristocrats too) attached to military victory. A European ruler such as Louis XIV could
tell his son that war was a means to “distinguish [kings] . . . and to fulfill the great
expectations ...inspired in the public.” The glory that European rulers attached to warfare
stook in sharp contrast to the goals that rulers were supposed to pursue in at least one
other part of the world–China. There, the Ming emporers advised to focus on peace and
use force as a “last resort.”
Europeans who traveled to China and knew it well were
struck by the difference. One of them–the Jesuit missionary Matteo Ricci, who died in
Peking in 1610 after spending 28 years in China–noted that although the China could
easily conquer neighboring states neither the emperors nor Chinese officials had any
interest in doing so. “Certainly, this is very different from our own countries [in
Europe],” he noted, for European kings are “driven by the insatiable desire to extend their
The eighteenth-century historian Edward Gibbon invoked the competition
between European states to explain the West’s military prowess; so has the modern
military and diplomatic historian, Paul Kennedy (Black 1998, 3-7; Kennedy 1989 ). But
their insights could be pushed further using economic theory, which could explain why
the competition led to productivity gains in the military sector. The key is to model the
military competition among the European states as a research tournament in which the
prize for the victor would foster high rates of military innovation. Without competition,
no state would have an incentive to innovate, but if more than one state was willing to vie
for the prize, the tournament could push states to devote enormous effort to military
innovation. Some rulers would off course choose not to enter the tournament, and in
equilibrium one would expect that only states that could exert themselves at low cost
would engage in military competition. But so long as you had two states competing, you
could still elicit arbitrary high levels of effort devoted to innovation, and two competitors
would in fact be the cheapest way to reach any given level of effort if you were in fact
designing such a tournament.
Western Europe of course often had two states or blocks
of states at war with one another in the late medieval and early modern period, such as
France versus the Habsburgs in the sixteenth and seventeenth-centuries, or France and
England in the eighteenth century.
If the tournament was the driving force behind the technical change in the military
sector, then it could also be considered as the cause of western Europe’s comparative
advantage in violence. The political incentives created the tournament, and the
tournament in turn led to enormous spending on warfare and unceasing efforts to improve
the technology of artillery, firearms, fortifications, and armed ships. It is no wonder that
western Europe came to dominate this technology.
The same argument also fits certain other parts of the globe. It seems to work for
Japan, where advances such as volley fire came during a period of incessant warfare
among clans and warlords that is reminiscent of the European tournament among kings
and princes. When the country was unified under under the Tokugawa shogunate, the
warfare came to and end, as did the military advances.
The argument corresponds to what we know about China too. There it was clear
to both Chinese and western observers in the 1500's and 1600s that China’s military
technology lagged behind Europe’s (Chase 2003, 142). Yet China had been quite
inventive earlier; indeed, it was the birthplace of both gunpowder and firearms. What
marks China’s innovations, though, was that they came precisely during periods when the
Chinese Empire itself was fragmented or non existent and rival powers were fighting
with one another under conditions very much like those in Europe.
As the military
historian Kenneth Chase has noted, the Chinese discovered crossbows and trebuchets
before the Empire was unified in 221 BC. They began to use heavy cavalry during a
second period of disunity between 220 and 589, and two subsequent periods of
fragmentation (756 to 960 and 1127-1276) witnessed the invention of gunpowder and
firearms (Chase 2003 , 32-33). But for nearly three quarters of the two millennia
between 221 BC and the nineteenth century, the Chinese Empire was intact, which may
have lessened the incentive to create new military technology. Western Europe, by
contrast, spent much more time fragmented into warring states. After the fall of the
Roman Empire, western Europe knew only two short lived empires (the Carolingian and
the Napoleonic), and it thus lived through a millennium and a half of nearly uninterrupted
One might argue that the Chinese emperors could conceivably have encouraged
military innovations simply by offering prizes to inventors. That way the emperors could
have better weapons without wasting resources in war. But even if the emperors had
tried this, the offer of a prize might not have seemed credible to someone who made a
better cannon or devised promising military tactics. Military innovators in China had no
one else to turn to if they wanted to commercialize their ideas. They would have had a
hard time selling their ideas abroad, and they would not find it easy to interest private
purchasers either, for private ownership of weapons was restricted. (The Ottoman
Empire imposed similar restrictions on private gun ownership.) In Europe, by contrast, a
better cannon could be sold to a private merchant or to a foreign army or navy, and there
was even an international market in Europe for military skills and tactical knowledge, in
which mercenaries and skilled craftsmen such as gun founders were hired away by other
Another force for productivity growth was the ease with which information about
new military technologies and tactics spread in early modern Europe. European
mercenaries and migrant craftsmen transmitted information from state to state; so did
books written by commanders and military engineers. (One could say the same of
captured ships and weapons and of tactics revealed in battle.) The new technology
spread quickly and was available at a competive price, as if the tournament served as an
idealized prize system that quickly put winning ideas into the public domain. If we
consider technology as a plan that can be used over and over again, all this spread of
information would lead to increasing returns, as in models of endogenous growth.
same thing would happen when states drew up plans of successful ships and built
templates and models of innovative weapons–all things that happened as early as the
seventeenth century. And yet despite the increasing returns and the competition among
states, all the progress in the military realm would fail to ignite economic growth overall,
because warfare interfered with trade and destroyed enormous amounts of capital in other
parts of the economy.
Here one could even ask whether the military competition in Europe actually
delayed economic growth by diverting talent and resources to destructive activity. Joel
Mokyr (1990 , 183-86) has argued persuasively that warfare did not spur technical
change in the civilian economy, but perhaps the toll war took was even greater than he
supposed. A careful assessment would have to take into account the occasional positive
technological spillovers from the military sector (in areas such as metal production), and
it would have to acknowledge that borrowing for warfare helped create European
financial markets. But it would also have to determine whether the tournament among
Europe’s rulers led to massive overinvestment in the military sector in what were poor
economies. What would have happened to the western European economy if the
resources and talent that worked such wonders in the military sector had instead been
allocated to the civilian economy? Could the resources and talent (and even perhaps
some technology) found ready application in the civilian sector? If so, could this help
explain why western Europe industrialized rapidly after 1815, when a century of relative
peace allowed talent and inventive effort to shift to the civilian uses?
Those are interesting questions for economic history, but what can the price
trends contribute to military history? In particular, what do the prices say about the
military revolution? Military historians have debated when exactly the revolution began
and precisely what technology and tactics were involved. The influential historian
Geoffrey Parker has claimed that there was such a key technology, and in his view, it and
associated tactics appeared at the end of the fifteenth century and then spread throughout
much of western Europe over the next two hundred years, giving Europeans an advantage
that allowed them to dominate the rest of the world. For Parker, the technology is clear:
it consisted of siege artillery and handguns, thick earthwork fortifications that could resist
bombardment (the so called trace italienne), infantry soldiers trained to fire their muskets
in volleys, and sailing ships armed with cannons. Other historians disagree about the
timing or the nature of the technology. They argue that the military revolution spread out
over a longer period or that western Europe experienced repeated revolutions in tactics
and technology between the end of the Middle Ages and the early nineteenth century,
beginning in the fourteenth century, when knights on horseback were supplanted by
archers and infantry troops with pikes (Black 1991; Rogers 1993; Parker 1996).
The price data cannot speak to the question of tactics, but evidence for sustained
technical change does support the historians who believe that the improvements in
military technology were spread over a longer period or that there were repeated military
revolutions. And if the tournament between rulers was the driving force behind the
ongoing technical change in military production, it would provide a theoretical
explanation for what one military historian has called “punctuated” equilibria: repeated
improvements in technology and tactics that gave one state an advantage and then were
imitated, leaving a new status quo (Rogers 1993). The reason is that other states would
eventually imitate successful military innovations, and when they did so, there would be
a new equilibrium that would last until another state discovered better tactics or
technology. The Dutch, for instance, invented volley fire in 1594 and put it into practice
beginning in 1599. The new tactic was described in print as early as 1603, and books
explaining it quickly appeared in several languages. It was also spread by foreigners who
served in the Dutch army and by Dutch military instructors who taught the tactic to states
allied with the Dutch.
Other western European states then adopted volley fire, reducing
the military advantage the Dutch had.
Military history also offers an alternative explanation for Europe’s comparative
advantage in violence–geography. The military history Kenneth Chase maintains that
China had no reason to develop firearms because its enemies were typically horse riding
nomads from the steppes of Asia, who fought with bows and arrows and depended on
their mobility, rather than any advanced technology. The steppe nomads had no fortified
cities to attack with artillery, and firearms were useless against them, for they had to be
pursued on horseback and it was impossible for a rider to shoot early hand guns (apart
from pistols, which had a very short range) with any effectiveness. A similar argument
would apply elsewhere as well. Eastern Europeans, for instance, faced similar enemies
from lands further East along with more heavily armed western Europeans, and so they
too had less of an incentive to develop firearms. The same would hold for the Ottomans
(Chase 2003).
If we pursue this geographic explanation a bit further, though, we can perhaps get
it to complement the argument about the tournament among rulers. The reason is that the
geography is not merely a matter of climate, density of population, and agricultural
endowments, which are what Chase stresses. It is also a matter of politics. If the Chinese
Empire had disintegrated into separate states, then the ones away from the interior would
have faced enemies who were not steppe nomads, but warriors who could have developed
very different military technologies. Similarly, if western and eastern Europe had been
unified into an Empire, then their common enemy might have been steppe nomads, or
powers like the Ottomans, who had to had to spend at least some of their resources
fighting nomads. In that case, the western Europeans would have the tournament with
one another, and they would probably never have developed their formidable military
technology. The big question then would be what held China together and what kept
western Europe from coalescing into a cohesive Empire. That is the question we may
have to answer if the conclusions from the meager price data hold true.


Let L = w
x - λ(f(x, t) - y) be the Lagrangian of the firm’s cost minimization problem;
here x represents a vector of factors of production, which are chosen to minize cost; w is
the vector of their prices; f(x, t) is the production function, which depends on time t since
we are considering technical change; y is output produced; and λ is the Lagrange
multiplier, which by the envelope theorem equals the marginal cost of production when x
is chosen optimally. Let c(w, y, t) be the firm’s cost of producing y once x is chosen
optimally; by the envelope theorem, the partial derivative of ln(c) with respect to time
= −
λ ∂
λ ∂
ln ( )

which equals the rate of technical change times the ratio of marginal cost to average cost.
Since free entry drives the firms to produce at minimum short run average cost, each
firm’s marginal cost will equal its average cost, and the rate at which c is declining will
therefore equal the rate of technical change (the rate at which the production function is
shifting out). Furthermore, since the firms are small relative to the size of the market, in
the long run the industry supply curve will be flat at a price p equal to this minimum short
run average cost. For each firm, c will therefore equal p y, and the partial derivative of ln
c(w, y, t)
with respect to time will be
ln (
ln ( )
p y

Since the long industry supply curve is flat, the price p will be independent of how much
output firms produce and thus will be function of w and t alone. At any time t it will have
to equal an individual firm’s marginal cost, and since it is independent of y, we can
assume that as a function of w it can be derived from a constant returns cost function,
with c(w, y, t) = y c(w , t). If (as in the body of the paper) we use a constant returns
Cobb-Douglas cost function as a first order approximation to this cost function and
assume that the rate of change of c(w, t) is constant over time and cost neutral, then
ln (p) = ln (c(w, t)) = a - bt + s
ln (w
+ . . . + s
ln (w
where a is a constant, b > 0 is the rate of technical change, s
and w
are the factor share
and price of the i-th factor of production, and factor shares have to sum to one. We can
then calculate b by regressing ln(p) on time and on the logarithms of the factor share
prices; the error term in the regression will represent short term deviations from our
numerous assumptions (cost minimization, U-shaped cost curves, open entry, small firm
size, competitive factor markets, Cobb-Douglas cost function, and cost neutral technical
change). We assume as well that these error terms are identically distributed and
One additional concern with these regressions might be what would happen to
prices if the state acted as a monopsonist. This will not be a problem, for two reasons.
First of all, states were not monopsonists in most of western Europe. There were in fact
many private buyers of arms and gunpowder besides the state: military contractors
bought them, as did privateers merchants, city governments, and even colleges. Second,
under our assumptions, even if the state is a monopsonist, the industry supply curve will
continue to be flat at the minimum average cost. Weapons producers will not produce
anything unless the price they receive at least this minimum average cost, and no
monopsonist will ever choose a higher price. The price will continue to equal c(w, t), and
the results of the price regressions will be unchanged.

Table 1
Index of Prices Relative to Skilled Wages
Military Good
Final Price Relative to Skilled
Wages (Index, Starting Date = 100)
Initial Final Good Iron Copper
Implied Lower
Bound for Rate of
Change (% Per
Artillery 1476
Muskets 1451
Artillery 1382
Muskets 1620
Pistols 1556

Source: England: Beveridge 1965 (prices of firewood), Phelps Brown and Hopkins 1955
(building craftsmen’s wages), Tout 1911 (prices of artillery in 1382-88), Rogers 1993
(prices of artillery in other years), and Rogers and Rogers 1866-1902 (prices of other
guns and of iron and firewood). For France: Avenel 1968 (prices of guns), Guyot 1888
(iron prices and prices of fir planks), Levasseur 1893 (mason’s wages, copper prices).

Note: For France, wages (for masons) are 25-year averages, as are prices of iron, copper,
and wood. Levasseur’s figures would have changed the final relative price of iron for
artillery from 115 to 76, but his iron prices are less reliable than Guyot’s. For England,
prices of iron (wrought iron) and firewood (fagots) are 25-year averages. Here and in
subsequent tables, the French artillery include canons, couleuvrines, serpentines, and
pieces de canon. I used only those prices for which d’Avenel had converted the prices to
francs per kilogram in order avoid problems with different units of weights. Handguns
included arquebuzes, fusils, and mousquets; if the context made it clear that the
mousquets or arquebuzes were large caliber, they were excluded. I also excluded guns
that were made for ornament or collection. As explained in the text, the flintlock fusils,
which appeared in the late seventeenth century, represent a qualitative improvement;
including them in the table will therefore underestimate technical change. To calculate
the implied lower bounds for the rate of technical change, I assumed that the labor factor
share was 0.5 and then chose the factor price in the table that would yield the lowest rate
of technical change between the initial and final date if prices for all the factors of
production other than labor had risen at the same rate relative to wages. Labor shares
from 0.25 to 0.75 lead to similar results.

Table 2
Coefficients of Time in Regression of ln(p/q)
Good with
Price p
Good with Price
Period Time
(Percent Per
Factors of
Production in
Addition to
Skilled Labor
Time Coefficient/ T-
Statistic with No
Other Factors of
Production in

Lathing Nails 1476-1690 -0.2 / 2.22
Lathing Nails 1475-1792 -0.5 / 1.55
Iron, Capital -0.1 / 0.71
Gunpowder Lathing Nails 1359-1765 -0.3 / 1.95
0.1 / 0.75
Artillery Spades
1382-1439 -2.4 / 8.65
Muskets Spades
1620-1678 -1.6 / 3.49
1556-1706 -1.1 / 4.85
Iron, Capital -1.3 / 8.33
Gunpowder Spades
1650-1706 -0.8 / 9.29
-0.5 / 8.53

Source: English spade and gunpowder prices were kindly furnished by Greg Clark; the
English rent charge prices used in calculating the rental cost of capital came from his
2002 article. The French lathing nail and gunpowder prices are from d’Avenel, and the
legal maxima interest rates used in calculating the cost of French capital came from
Guyot 1784-85, s.v. “Rente”. All the other prices come from the sources listed in Table

Note: See text for explanation of regressions; the negative coefficients are a sign of
technical change, and N is the number of price observations for the military goods.
Where there were more than 10 observations, I ran the regressions on the year alone and
with additional factors of production other than skilled labor. The other factors of
production were ones whose prices I could find and for which factor shares were likely to
different for the military good and the comparison good. It was difficult to find prices for
the military and non military goods on the same date, and for that reason, I calculated the
price of the non-military goods by computing averages over long periods. In particular,
for France, the lathing nail prices (from d’Avenel) were averages over 50-year periods;
iron prices and masons’ wages (both from Levasseur) were averages over 25-year
periods. There were no lathing nail prices available for 1650-99. Capital rental prices
took the legal maximum on perpetual annuities as the interest and assumed that the sales
price of capital goods was proportional to labor and that depreciation was 10 percent.
Capital rental prices for English goods were calculated in the same way, except that
Clark’s decennial averages for rent charges were used for interest rates. Prices of iron
and spades were 25-year averages. The price of gunpowder was clearly influenced by
warfare; the table does not take that into account.

Table 3
Regression of the relative price of early handguns in Frankfurt on time and the price of
Coefficient in equation 2 and
associated explanatory variable
Coefficient T-statistic
a (the constant term)
b (the year; the opposite of the
coefficient is then the total
factor productivity growth rate)
-0.030 5.92
(the logarithm of the price of
copper relative to the skilled
wage; the coefficient is then the
factor share for copper)
0.307 1.98
R-square 0.73
Adjusted R-square
Standard error
Observations 21

Source: Rathgen 1928, 68-74.

Note: The regression covers the years 1399-1431. The dependent variable is the
logarithm of the price of the handguns divided by the skilled wage. The wages used were
actually a piece rate (the money paid to the metal worker to cast a pound of copper). If
metal workers got better at casting in general, then the regression would underestimate
the rate of productivity increase. For some of Frankfurt’s purchases, the accounting was
incomplete, and Rathgen had to assume that the wage rate or price of copper was the
same as in other transactions at nearby dates. I have used the prices he calculated for the
handguns except in a few instances where his extensive quotes from the archives suggest
that the prices were different; these differences were always small. As noted in the text, I
have assumed that the interest and depreciation rates were constant and that the sales
prices of capital was proportional to the skilled wage. The rental price of capital relative
to the skilled wage is then constant, and its coefficient enters into the constant term.


Table 4
Military Labor Productivity in the French Army:
Rate of Successful Fire per Infantryman, 1600-1750
Approximate Date Rate of Successful
Fire per Handgun
Handguns per
Rate of Successful
Fire per
1600 (1620 for
handguns per
0.25 to 0.50
0.5 to 1 shot per
minute with
matchlock; 0.50
misfire rate
1 shot per minute
with flintlock, 0.33
misfire rate;
bayonets have led
to replacement of
1.33 1.00 1.33
with flintlock,
ramrod, and paper
cartridge; 0.33
misfire rate.

Source: Lynn 1997, 457-60, 464-65, 469-72.

Notes: The calculation considers only pikemen and infantrymen with firearms; it ignores
unarmed solders, such as drummers. The implied rate of labor productivity growth over
the 150 year period from 1600 to 1750 is between 1.3 and 1.7 percent per year.
Table 5
Probability That a Major European Sovereign Was Deposed After Losing a Foreign War
Fraction Deposed Because of Defeat in
Each Year of War or in Each Year of
War Loss
Conditional on:
Being at War
Losing War
Period: 1500-
Austrian Dominions
France 0.00
Great Britain
Hohenzollern Dominions
Spain 0.00
Source: Langer 1968; Hoffman and Rosenthal (2002).

Note: The calculation of the conditional probabilities begins with a count of sovereigns
who were deposed after losing a foreign war for the Austrian Dominions, France, Great
Britain, the Hohenzollern lands, and Spain. The count includes any assassinations
provoked by loss in a foreign war, but it excludes assassination or removal from office
during civil wars and internal revolutions, unless the cause was the loss of a foreign war.
In particular, the executions of king Charles I of England and Louis XVI of France are
not counted, and the same holds for the removal of James II of England and the
deposition of Ferdinand II in Bohemia in 1618. The calculations also exclude the simple
downfall of ministries. The number of deposed monarchs is then divided by the number
of years the country was at war; that yields the probability of deposition after losing a
foreign war conditional on being at war. War here is defined as any class of armed
conflict significant enough to be included in Langer 1968; no formal declaration of war is
necessary. It includes colonial fighting, but it excludes civil wars unless foreign powers
are involved. The calculation of the probability of deposition conditional on losing a war
is similar; the only difference is the number of deposed monarchs is divided by the
number of years in which a war ended with a loss for the country concerned. Sovereigns
included all monarchs, whether absolute or constitutional. For republics, the sovereign
was the parliament or legislative assemblies; if the legislative assemblies shared
sovereignty with a president or other executive, then the sovereign was the executive and
the legislative assemblies together.
The Austrian dominions exclude Habsburg territory in Iberian Peninsula, Italy,
Low Countries, and Latin America. Bohemia is excluded before Habsburgs assume the
crown in 1526, and Hungary is not counted until it was fully integrated into the Habsburg
holdings in 1699. For France, the Convention is counted as a sovereign; Napoleon's
abdication in 1814 is counted as a removal after a loss, but not his second abdication after
Waterloo. For Great Britain, the calculation concerns England and Ireland alone up until
1603; during the Protectorate, the Lord Protector is counted as sovereign. For Spain,
depositions do not include loss of Portugal or of non-Iberian possessions. All the
probabilities are ex-post, and they clearly make more sense for monarchies than for

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Figure 1. Prices relative to mason’s wages: French artillery
Prices Relative to Mason's Wages: French Artillery
1476 war
1524 war
1622 peace
1647 war
1690 war
1476 = 100
cannons (per kg)
iron/wages Levasseur
iron/wages Guyot

Figure 2: Prices Relative to Mason’s Wage: French Muskets
Prices Relative to Mason's Wage: French Muskets
25-year period beginning
1451-75 = 100

Figure 3: Prices Relative too Skilled Wages: English Artillery
Prices Relative to Skilled Wages: English Artillery

Figure 4: Prices Relative to Skilled Wages: English Muskets
Prices Relative to Skilled Wages: English Muskets
1620 = 100

Figure 5: Prices Relative to Skilled Wages: English Pistols
Prices Relative to Skilled Wages: English Pistols
1556 = 100

Figure 6. Prices of cannons and capital relative to a mason’s wages in France, 1476-
1690. There are two measures of the price of capital in the figure: the rental price of
housing, and the rental price of a capital good whose sales price is proportional to
mason’s wage. Both are measured relative to the mason’s wage. For the second good, I
have assumed 10 percent depreciation and an interest rate r equal to the legal maximum
on perpetual annuities.
Price of Cannons and Capital Relative to Mason's
Wages in France, 1476-1690
1476 war
1524 war